PRP Records

Probable Primes Top 10000

(247113 PRPs in the top)


What is a PRP ?

A PRP is a probable prime number, a number that nobody knows how to prove or disprove its primality.
Here are some criterions that can be used to recognize these numbers :

- N does not have any prime factor up to 2^32.
- N cannot be trivially written into a product.
- Take 3 square-free consecutive bases such that (b1/N)=(b2/N)=(b3/N)= -1. N should be such that b1^((N-1)/2)=b2^((N-1)/2)=b3^((N-1)/2)= -1 (mod N).
- Take a prime base such that (b/N)= -1 and b<>b1<>b2<>b3. N should pass the strong test in base b.
- or more (if someone has got an idea) !!!


Submit your PRPs


See the Top discoverers
See the Latest PRPs
Search by form



1-250   251-500   501-750   751-1000   1001-1250   1251-1500   1501-1750   1751-2000   
2001-2250   2251-2500   2501-2750   2751-3000   3001-3250   3251-3500   3501-3750   3751-4000   
4001-4250   4251-4500   4501-4750   4751-5000   5001-5250   5251-5500   5501-5750   5751-6000   
6001-6250   6251-6500   6501-6750   6751-7000   7001-7250   7251-7500   7501-7750   7751-8000   
8001-8250   8251-8500   8501-8750   8751-9000   9001-9250   9251-9500   9501-9750   9751-10000   


Rank Probable prime Digits (> 30000) Who ? When ?
97512^175045+19552694Lelio R Paula02/2011
9752195^23010-252694Lelio R Paula10/2017
97532^175025+14952688Lelio R Paula02/2011
9755(19^41201+1)/2052685Paul Bourdelais03/2010
9754(436*10^52683-13)/952685Robert Price10/2017
97562*12^48815-5^4881552681Mike Oakes10/2010
9757335^20862-20862^33552678Norbert Schneider09/2015
97582^174983-760552676Lelio R Paula07/2009
97594*10^52667+1952668Robert Price04/2016
9760(10^52667+77)/352667Robert Price01/2017
976111434^12977+12977^1143452664Norbert Schneider04/2016
97622^174941-120352663Lelio R Paula07/2009
97638501^13400-13400^850152655Norbert Schneider03/2018
97642^174910+1270552654Lelio R Paula07/2012
97653^110338+7452645Lelio R Paula10/2012
97665^75303+1252635Lelio R Paula10/2012
97672^174836+25525552631Lelio R Paula07/2009
9768(66^28921+1)/6752622Paul Bourdelais08/2017
976920^40443+952618Lelio R Paula01/2013
9770(11*2^174788+1)/952617Lelio R Paula01/2012
9771(11*2^174786-1)/70352615Lelio R Paula01/2014
977211^50520-129052612Enzo Doria11/2012
9773(670^18617-1)/66952611Eric Chen09/2018
9774(10^52608-19)/952608Robert Price10/2017
9775(9913*2^174736-1)/33352603Lelio R Paula03/2015
977613145^10024+10024^1314552594Hans Havermann05/2016
97775003^14217-15052592Enzo Doria07/2012
97782^174698-405552590Yves Minet02/2018
977919^41123+1052587Lelio R Paula01/2013
97802^174683+1290952585Lelio R Paula01/2011
97812^174643+5952573Lelio R Paula01/2011
9782(1017*2^174640-1)/77352572Lelio R Paula03/2015
978313529^7662+7662^1352952552Hans Havermann06/2016
9784121421#+18876752548Makoto Morimoto02/2016
978520^40375-592352530Enzo Doria03/2013
9786(67607*2^174503+1)/9094807952528Lelio R Paula05/2014
9787(-lucasV(1,2,349014)+2)/(7*50873*1047043)52521Mike Oakes03/2017
97882^174462+34552519Lelio R Paula07/2009
9789t(178863)52509Robert Price10/2014
97902^174416+85552505Lelio R Paula07/2009
97916^67467-10352500Lelio R Paula10/2012
9792(2^174533-1)/(193594572654550537*91917886778031629891960890057)52494Dario Alpern06/2017
97937888^13467-13467^788852481Norbert Schneider05/2018
97942^174329-1126552479Enzo Doria06/2014
97952^174314-124152474Yves Minet05/2009
979652^30577-5152471Norbert Schneider08/2014
97979403^13206-13206^940352471Norbert Schneider12/2017
979815692^2205+2205^1569252465Hans Havermann06/2016
9799(2^174281-7)/62881702961552453Lelio R Paula02/2012
9800(2^174240+5)/352451Lelio R Paula02/2012
9801(86*10^52450-221)/952451Robert Price06/2017
9802(62*10^52448-197)/952449Robert Price10/2017
9803(15*2^174221+1)/40352445Lelio R Paula07/2012
980426313!2-3252443Robert Price10/2015
9805(3*2^174214-1)/374872952438Lelio R Paula01/2014
98062*3^109900-552436Lelio R Paula03/2014
98084159^14488-15052432Enzo Doria07/2012
9807(89*10^52431-71)/952432Robert Price11/2015
98092^174170-394152431Yves Minet04/2017
9810(7*2^174171-1)/68552429Lelio R Paula01/2014
98115375^14052-14052^537552420Norbert Schneider10/2018
9812(260137^9679+1)/26013852409Faysal YAtim03/2008
98132^174098+7952409Lelio R Paula01/2011
981435^33940-221452406Enzo Doria03/2013
981515^44557+252404Ray Chandler07/2011
98162^174049-43952394Yves Minet01/2012
98176^67329+11552393Lelio R Paula10/2012
98192^174041+26214552392Lelio R Paula07/2009
9818141^24377+252392Lelio R Paula05/2013
9820lucasU(285,1,21339)-lucasU(285,1,21338)52382Mike Oakes05/2009
98212^174001-595552380Lelio R Paula07/2009
9822lucasV(-1,2,347969)52375Mike Oakes02/2017
98233^109764-14052371Lelio R Paula10/2012
98242*3^109761+752370Lelio R Paula03/2014
98259863^13112-13112^986352370Norbert Schneider10/2017
9827(145^24229+1)/14652366Richard Fischer02/2018
98268094^13399-13399^809452366Norbert Schneider03/2018
98282^173944-11225352363Enzo Doria06/2014
98302^173940+111152362Lelio R Paula01/2011
9829(3126^14983-1)/312552362Richard Fischer03/2015
983115214^2763+2763^1521452358Hans Havermann05/2016
983213200^9247+9247^1320052352Hans Havermann05/2016
9833(1017*2^173867-1)/717552339Lelio R Paula03/2015
983413732^6465+6465^1373252327Hans Havermann05/2016
9835(2^173867-1)/5253663750268952326Donovan Johnson06/2005
98362^173811-68487752323Paul Bourdelais11/2012
98372^173807-595552322Lelio R Paula06/2009
98382^173796-104468952318Paul Bourdelais11/2012
983910^52317+6449752318Patrick De Geest12/2012
984010^52317+6474352318Patrick De Geest12/2012
984210^52317-7152317Robert Price05/2011
984110821^12968+12968^1082152317Norbert Schneider04/2016
9843(298*10^52308-7)/352310Robert Price06/2017
9844(2^173778-3)/5795952308Lelio R Paula02/2012
984510232^13043-13043^1023252302Norbert Schneider08/2017
98462^173727+952298Lelio R Paula01/2011
9847(14^45631+13^45631)/2752298Robert Price04/2013
984837856!3+656152293Robert Price11/2015
98494*3^109596+552292Lelio R Paula03/2014
985015436^2441+2441^1543652291Hans Havermann05/2016
985143^32005+2452280Robert Price11/2013
98522^173650-16552274Lelio R Paula02/2011
98534*10^52272+9352273Robert Price01/2017
985419^40873+8452267Lelio R Paula01/2013
98552^173621+424242952266Jason Earls09/2008
98569999^13064-13064^999952256Norbert Schneider09/2017
9857numbpart(46909^2-1)52247Serge Batalov04/2017
985814^45579-3152240Lelio R Paula01/2013
98597395^13502-13502^739552239Norbert Schneider05/2018
9860(10223*2^173518+1)/90352236Lelio R Paula05/2014
986120^40147-612352233Enzo Doria03/2013
98624^86754-3^(86754+1)52232Robert Price04/2016
98637452^13487-13487^745252226Norbert Schneider05/2018
98642^173477-343352222Yves Minet04/2009
9865(22*10^52217-73)/352218Robert Price09/2017
9866(25*2^173446+1)/6152213Lelio R Paula07/2012
98673^109431-3852212Lelio R Paula10/2012
98682^173424-395952206Yves Minet04/2017
986913^46861-7252201Lelio R Paula01/2013
98702^173373-136352191Yves Minet03/2009
987111^50114-174052189Enzo Doria11/2012
987213735^6304+6304^1373552188Hans Havermann05/2016
987311^50111-111052186Enzo Doria11/2012
9874lucasU(46,1,31387)+lucasU(46,1,31386)52181Mike Oakes04/2009
987520^40105-858352178Enzo Doria03/2013
9876(10322^13001+2679^13001)/13001^252175Lelio R Paula08/2008
98772^173314-394152173Yves Minet04/2017
98782^173294+115552167Lelio R Paula07/2012
9879(19*2^173301-1)/2348952166Lelio R Paula01/2014
988015146^2781+2781^1514652166Hans Havermann06/2016
988111^50088-3252162Lelio R Paula01/2013
98823^109320+23652159Lelio R Paula10/2012
98832^173246-2863552153Lelio R Paula06/2009
98842*10^52147+1152148Robert Price01/2015
98857605^13436-13436^760552147Norbert Schneider04/2018
98862^173208-11262552141Enzo Doria06/2014
9887(9179*2^173206-1)/203552141Lelio R Paula03/2015
988815^44333-7652140Lelio R Paula01/2013
98892^173187-318952135Yves Minet10/2014
98902^173167+7557952129Enzo Doria04/2016
9891(2^173169+7)/9279352125Lelio R Paula02/2012
9892(25*10^52119+23)/352120Robert Price06/2017
98939*7^61671+452119Lelio R Paula09/2014
98962^173130-922152118Lelio R Paula07/2008
9894(17*2^173129-1)/352118Lelio R Paula01/2014
98956482^13673-13673^648252118Norbert Schneider08/2018
9897215^22342-21652112Karsten Bonath04/2018
98982^173100-11255952109Enzo Doria06/2014
98992^173091-11233952106Enzo Doria06/2014
990070797!6-3252106Robert Price08/2018
990111^50030+2852101Lelio R Paula01/2013
9902(59*10^52099+13)/952100Robert Price09/2015
99032^173064-182952098Yves Minet09/2012
99042^173062-136152097Yves Minet08/2012
99053^109190-7052097Lelio R Paula10/2012
99062^173059+9019552096Lelio R Paula07/2012
99072^173048-11262552093Enzo Doria06/2014
990892^26524+9152088Norbert Schneider04/2013
990941^32295-4052085Theodore Burton02/2007
99102^173002+17752079Lelio R Paula02/2011
9911p(11334)#/2+852075Robert Price01/2017
99122^172965-11236352068Enzo Doria06/2014
99139*2^172935+752060Lelio R Paula03/2014
99145959^13790-13790^595952060Norbert Schneider10/2018
991511^49978-819052047Enzo Doria02/2013
991610^52041+63352042Patrick De Geest11/2012
99178494^13245-13245^849452042Norbert Schneider01/2018
991810^52041-9352041Robert Price05/2011
9919(21*2^172815-1)/86952021Lelio R Paula01/2014
9920(182*10^52018+1)/352020Robert Price02/2017
99214*6^66843-552015Lelio R Paula09/2014
99227732^13377-13377^773252014Norbert Schneider03/2018
992319^40670-5452007Lelio R Paula01/2013
99242^172756-11288352005Enzo Doria06/2014
992511832^12763-12763^1183251985Norbert Schneider02/2017
99267^61511-3651983Lelio R Paula10/2012
992710591^12914-12914^1059151979Norbert Schneider05/2017
99282^172640-7551970Lelio R Paula01/2011
99296792^13559-13559^679251959Norbert Schneider07/2018
99307750^13359-13359^775051958Norbert Schneider03/2018
9931gcd(V(932265),5*F(186453)*(F(186453)-1)+1)51953Serge Batalov04/2015
993212240^12709-12709^1224051952Norbert Schneider01/2017
9933t(173589)51951Robert Price12/2014
99347^61469+3451948Lelio R Paula10/2012
99359*2^172553-751945Lelio R Paula03/2014
993611542^12787+12787^1154251945Norbert Schneider01/2016
993735^33640-708651943Enzo Doria03/2013
9938(7*2^172534+1)/247951936Lelio R Paula07/2012
99397353^13430-13430^735351927Norbert Schneider04/2018
9940(2^86243+43467)^2+(2^86243+43467)+4151924Makoto Morimoto05/2016
9941(2^86243+84085)^2+(2^86243+84085)+4151924Makoto Morimoto05/2016
9942((2^86243+75146)^2+(2^86243+75146)+41)/6151922Makoto Morimoto05/2016
9943((2^86243+8692)^2+(2^86243+8692)+41)/301151920Makoto Morimoto05/2016
9944((2^86243+30085)^2+(2^86243+30085)+41)/41/19951920Makoto Morimoto05/2016
9945((2^86243+36540)^2+(2^86243+36540)+41)/43/64751920Makoto Morimoto05/2016
99472^172470+751919Lelio R Paula01/2011
9946((2^86243+76136)^2+(2^86243+76136)+41)/6050951919Makoto Morimoto05/2016
9948((2^86243+50999)^2+(2^86243+50999)+41)/249686951918Makoto Morimoto05/2016
9949((2^86243+80760)^2+(2^86243+80760)+41)/93048151918Makoto Morimoto05/2016
9950((2^86243+26732)^2+(2^86243+26732)+41)/223/9651751917Makoto Morimoto05/2016
9951((2^86243+51479)^2+(2^86243+51479)+41)/1607/2202751916Makoto Morimoto05/2016
99542^172455+1551915Lelio R Paula01/2011
9952((2^86243+27637)^2+(2^86243+27637)+41)/2693/51843151915Makoto Morimoto05/2016
9953((2^86243+82275)^2+(2^86243+82275)+41)/71/930992951915Makoto Morimoto05/2016
9955((2^86243+57757)^2+(2^86243+57757)+41)/30871/62272951914Makoto Morimoto05/2016
9956((2^86243+18643)^2+(2^86243+18643)+41)/47/23071/6529351913Makoto Morimoto05/2016
9957((2^86243+8693)^2+(2^86243+8693)+41)/494107/293389151912Makoto Morimoto05/2016
9958((2^86243+8250)^2+(2^86243+8250)+41)/223/34877/147262351911Makoto Morimoto05/2016
9959((2^86243+51745)^2+(2^86243+51745)+41)/71/95891/217129351911Makoto Morimoto05/2016
9960((2^86243+29592)^2+(2^86243+29592)+41)/7717/11933/1256650951909Makoto Morimoto05/2016
99615^74263+5451908Lelio R Paula10/2012
996213804^5755+5755^1380451904Hans Havermann05/2016
99637*2^172403-351900Henri Lifchitz06/2003
9964t(196078)51892Robert Price02/2014
99652*3^108759-751892Lelio R Paula03/2014
9966(94*10^51889+11)/351891Robert Price02/2017
9967(73*10^51889+17)/951890Robert Price10/2015
996835^33603-402651886Enzo Doria03/2013
99692^172350-10751883Lelio R Paula02/2011
997014419^3960+3960^1441951876Hans Havermann05/2016
99712^172325-11318551875Enzo Doria07/2014
997210^51872+10068351873Patrick De Geest06/2016
997310^51872-100000000151872Robert Price05/2016
997410^51872-10014951872Patrick De Geest06/2016
99752147092^8192+6351871Jens K. Andersen04/2009
997613^46564-2451870Lelio R Paula01/2013
997710524^12893-12893^1052451858Norbert Schneider05/2017
997813981^5110+5110^1398151848Hans Havermann05/2016
99792^172228+7626151846Enzo Doria04/2016
9980(59699!5-1)/2551840Joe McLean10/2018
998111^49772-126051833Enzo Doria11/2012
9982(11*2^172157-1)/35151823Lelio R Paula01/2014
9983(43*10^51816-403)/951817Robert Price04/2017
99849001^13102-11451810Enzo Doria07/2012
9985(80051^10567+1)/8005251809Faysal YAtim07/2007
99862^172101-6151808Lelio R Paula01/2011
9987(2^172125+3)/3112550551808Lelio R Paula02/2012
99889*7^61301+451807Lelio R Paula09/2014
9989(23*2^172090-1)/3650951802Lelio R Paula01/2014
99902^172074+145951800Lelio R Paula07/2008
99912^172063+16551797Lelio R Paula02/2011
9992(21181*2^172061+1)/1814751796Lelio R Paula05/2014
9993(56*10^51793+367)/951794Robert Price10/2017
999428^35785-2751787Norbert Schneider01/2014
9995(65*10^51778+43)/951779Ray Chandler09/2010
9996(15185*2^171975-1)/351774Lelio R Paula03/2015
99972^171978-11329751771Enzo Doria07/2014
999811^49708+7851766Lelio R Paula01/2013
9999(26*10^51764-107)/951765Robert Price07/2016
1000012^47956-9751754Lelio R Paula12/2012


Find by discoverer :


Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: December, 11 2018 05:54 (Time in France)

Go back
Valid XHTML 1.0!    Valid CSS!